薄板弯曲分析的多边形流形单元  

POLYGONAL MANIFOLD ELEMENT FOR THIN PLATE-BENDING ANALYSIS

作　　者：温伟斌[1] 骆少明[1] 

机构地区：[1]广东工业大学机电工程学院,广州510006

出　　处：《工程力学》2012年第10期249-256,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(50975050)

摘　　要：一般的数值流形方法均采用三角形、四边形单元进行计算。对于工程中的有些实际问题,多边形单元能更好的适应复杂计算域形状。为此,研究了采用多边形流形单元进行数值计算的方法。采用任意几何区域的Delaunay三角网格构造出新的凸多边形网格,并以此单元作为计算的流形单元。采用改进的Wachspress插值函数作为多边形流形单元的权函数。为说明该方法的有效性,将该流形方法应用于薄板弯曲计算,推导出用于薄板弯曲分析的流形格式和单元矩阵。计算结果表明:较一般有限元法,计算精度和收敛速度有很大提高。A triangular or rectangular element was used for the numerical computation in a general numerical manifold method（NMM）.For many practical problems,a polygonal element can adjust to the complicated configuration of a computational domain easily,hence a polygonal manifold element is analyzed for numerical computation.The convex polygonal mesh for a manifold element is constructed based on a Delaunay triangulation mesh.An improved Wachspress shape function is used as a weight function of the numerical manifold method.The validity of the proposed numerical manifold method is illustrated by the analysis of a thin plate bending problem.Numerical manifold formulas and element matrices are also derived for the numerical example.The results show that this method,compared with the finite element method,can improve accuracy and convergence greatly.

关 键 词：数值流形方法 流形单元 多边形单元 薄板弯曲 权函数 

分 类 号：O343[理学—固体力学]